We are drawing a 5-card hand from a standard 52-card deck a. What is the probability that all the cards are spades? (5pts)

0.0005 = 0.05% probability that all the cards are spades.

Step-by-step explanation:

The cards are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

In this question:

52 cards means that N = 52.

13 of the cards are spades, which means that k = 13.

5 card hand means that n = 5.

What is the probability that all the cards are spades?

This is P(X = 5). So

0.0005 = 0.05% probability that all the cards are spades.